Exploiting fascinating quantum properties for novel technical applications is appealing but still a dream. However, fundamental understanding of quantum systems and their behavior can be obtained by high-resolution imaging of model systems, such as ultracold quantum gases. The limitations of the current generation of such quantum gas microscopes restrict accessible regimes and applications. The IOF 'CavityMicroscope' will develop a novel microscope, based on sensitive detection of atoms evolving within a high-finesse optical cavity. Within CavityMicroscope the fellow will combine two lines of expertise, which he will acquire in the outgoing and return phase, overcoming current limitations. In the outgoing phase, CavityMicroscope builds upon the exceptional expertise in ultracold gases trapped in high-finesse cavities of Prof. Stamper-Kurn, Berkeley (USA), who is a leading scientist in the field. Designing a cutting-edge experimental setup and implementing cavity-aided imaging techniques will allow for non-destructive imaging, in three dimensions, of a quantum gas with single lattice-site resolution and single-atom sensitivity.This ground-breaking approach to quantum gas microscopy will promote EU research in this field during the return phase with Prof. Widera, Kaiserslautern (GER), who is an outstanding researcher regarding quantum systems and impurities in ultracold gases. Finally, CavityMicroscope will be used to non-destructively study and steer the dynamics of impurities in quantum systems. The complementary expertise of both hosts provides the fellow with a unique possibility to develop a novel research niche, pioneered by CavityMicroscope. In combination with the complementary training, this IOF will help the fellow to obtain scientific maturity and to actively shape research in quantum systems, which is a rapidly emerging field. Thereby, the IOF perfectly consolidates the fellow’s long-term aim to reach an independent research position in science in Europe.